# Seventh-order Korteweg–de Vries equation

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The seventh-order KdV equation is a nonlinear partial differential equation in 1+1 dimensions related to the KdV equation.[1] It is defined by the formula

${\displaystyle u_{t}+6uu_{x}+u_{xxx}-u_{xxxxx}+\alpha u_{xxxxxxx}=0.}$

where ${\displaystyle x}$ and ${\displaystyle t}$ are real variables and ${\displaystyle \alpha }$ is a constant.

## References

1. ^ Andrei D. Polyanin,Valentin F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Second Edition, SECOND EDITION p. 1040 CRC PRESS